Fluid Mechanics Ideal Flow Problem

[Wildcat04]

Homework Statement

Calculate flow velocity and magnitude at a point (2,-2)

Sink at origin with strength 20 m²/s
Vortex at (0,2) with strength 25 m²/s
Uniform flow in +x with strength of 10 m/s

The Attempt at a Solution

\phi = \phi1 + \phi2 + \phi3

\phi1 = -Ux = -U r cos(\theta)
\phi2 = -\mu_s ln r
\phi3 = \mu_v \theta

v_r = d\phi/dr
=-U * cos \theta - \mu_s * (1/r)
=-10 cos(\pi/4) - 20 / 2.83
=-14.14

v_\phi = (1/r) d\phi / dr
= (1/r) (-14.14)
= -5

u = .5 (14.14) + .5(5) = -9.57
v = -.5(14.14) + .5(5) = 4.57


I know that I have butchered this because the solutions is supposed to be

V = 12.5 m/s
u = 10 m/s
v = 7.5 m/s
\alpha = 37 degrees

Could someone please point out the obvious flaw in my logic and point me in the right direction?

Thank you very much in advance!

 

[Wildcat04]

Nevermind! I was making this problem a lot harder than I thought it was. I took a step back and looked at the units that I needed for my solution along with what the correct solution and was able to work it out.